The problem with maths and the rules
Why did I get this wrong in my assessment? 4 + 5 x 2 = 18. Doesn’t it? My teacher told me the answer is 14. The calculator on my phone says 14, my scientific calculator says 14 but a friend’s basic calculator says 18. Who’s right and who’s wrong?
As a parent we might agree with our child that they are correct – tell them the calculators and the teacher are wrong. That you agree with them because 4 + 5 is 9 and double 9 is 18. But, then you might remember a rule from school about the order of operations, but you can’t fully record the rules and so this is where I hope I can help.
BODMAS, BIDMAS, PEDMAS
My title shows a universal mathematical language. BODMAS, BIDMAS, PEDMAS and on research I’ve just discovered BEDMAS! These rules are used internationally, that’s the thing with Maths, it has it’s own language which can be used around the world.
The words are acronyms and represent the order of operation in Maths.
BOGOFF (not literally of course) but “buy one get one for free”. I am sure ROYGBIV has a meaning to you , it hopefully helps you remember the colours of the rainbow. For those mumsnet readers, a whole host of acronyms are used out there. In the same way BODMAS has a meaning that needs to be learnt and used to help your child learn in maths.
Why was 18 not the right answer?
In maths we use a specific order of operations, the acronyms are there to remind you.
B – brackets first
O – order of operation (more explanation to follow)
D – division
M – multiplication
A – addition
S – subtraction
The O is sometimes replaced with I for indices (which perhaps makes more sense…?) and if you’re in the USA the P is parenthesis and E is exponential!
The acronym tells us the order in which we complete a problem. I will explain more later.
The order of operations
We now know what the letters represent, we know the order in which they go. Otherwise, the word BODMAS (which I will use more commonly) would have a different spelling. But the reason they spell the word BODMAS is because they then explain the order of operations that we complete a sum.
With this in mind our original question 4 + 5 x 2 would become
5 x 2 = 10
10 + 4 =14
because M(ultiplication) is more powerful than A(ddition) and so we complete the multiplication first.
What is mummymaths from Solihull currently talking about?
Well let me use another example to explain.
Imagine you had £10 and someone kindly gave you another £10. Each week for three weeks, the same thing happens, you have £10 and someone gives you £10. (You’re not spending any of the money, it goes in a little pot) How much money do you have at the end of the three weeks?
Here’s the maths…
£10 + £10 = £20
£10 + £10 = £20
£10 + £10 = £20
Then in week 4 someone gives you an extra £30
Total amount £20 + £20 + £20 + £30 = £90
Let’s think about this mathematically
Each week we have £10 we add £10 and we get this for three weeks. Then in week four someone gives you £30. Mathematically we could write this as:
10 + 10 + 10 + 10 +10 + 10 + 30 = 90
(10 + 10) + (10 + 10) + (10 + 10) + 30 = 90
(10 + 10) x 3 + 30 = 90
3 x (10 + 10) + 30 = 90
All methods give the same solution but can you see the importance of the order because if we didn’t consider the order we might think we had £660…
30 + 3 x (10 + 10)
(this is (10 + 10) x 3 + 30 = 90 rearranged)
30 + 3 = 33
10 + 10 = 20
20 x 33 = £660 (oh, if only)
BODMAS tells us the importance of the order in which we do things. I might tell my students that the brackets are the most powerful and we do them first! The order is the power the second most important thing. Followed by division and multiplication then addition and subtraction, we always read the four basic operations from left to right.
We need to think BODMAS in all sums but in a test you need to remember it whenever you see a sum with a chain of operators, brackets and powers!
Always look out for BODMAS
Knowing what the letters stand for is fantastic but really understanding BODMAS is about application. It is just one of those things you need to remember and look out for. There will always be that hidden question waiting to catch you out on your exam paper. I suspect it might even be a multiple choice question…?!